Select all true statements (pick 3)
A. ∠3 ≅ ∠2 because they are alternate interior angles.
B. m∠1 + m∠3 = 180 because they form a straight angle.
C. ∠3 ≅ ∠6 because they are alternate interior angles.
D. ∠1 and ∠6 are supplementary because ∠3 ≅ ∠6 and m∠1 + m∠3 = 180.
E. ∠1 ≅ ∠3 because they are vertical angles.

The share Kyle sells worth $55000 and Kyle's gain amount is $5000

Given,

The share bought by Kyle of company XYZ = $50,000

The share price = $100

The  share price after an year = $110

We have to find the gain amount by Kyle when Kyle sells all his shares.

Here,

We can apply Unitary method;

100 ⇒ 110

50000 ⇒ x

Compute;

100x = 110 x 50000

x = (110 x 50000) / 100

x = 110 x 500

x = $55000

Now,

Kyle gains,

55000 - 50000 = $5000

That is,

The share Kyle sells worth $55000 and Kyle's gain amount is $5000

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The original price of desk bought by kevin is $780.

What is original price?

To calculate the initial worth of a reduced or sale item, you wish to grasp the sale worth and also the discount proportion. The calculations embody an easy formula that divides the sale worth by the results of one minus the discount in proportion form.

Main body:

Let the original price of desk be x.

After sale price of desk - $280.80

According to question, 36% of original price is what kevin bought it for.

So the equation formed is,

⇒36% of x = 280.80

⇒0.36*x = 280.80

⇒x = 280.80/ 0.36

⇒x = $780

Hence the original price of desk is $780.

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Rectangular coordinates are x = -3.5 , y = 7[tex]\sqrt{3}[/tex]/2 by using the relation between rectangular and polar coordinates

What do you mean by rectangular coordinates?

Rectangular coordinates, commonly known as cartesian coordinates, are a way to represent graphs and show where points are located on a two-dimensional surface or in three-dimensional space.

The origin is the intersection of the two perpendicular axes that make up the Cartesian plane.

The xy plane is another name for the Cartesian plane.

Given polar coordinates are (-7,5π/3)

To change polar coordinates to recatngular coordinate use

x = rcosθ , y = rsinθ

here r = -7 and θ = 5π/3

x = -7cos5π/3 = -7 × 1/2 = -7/2 = -3.5

y = -7sin5π/3 = -7 × -[tex]\sqrt{3}[/tex]/2 = 7[tex]\sqrt{3}[/tex]/2

Therefore, rectangular coordinates are x = -3.5 , y = 7[tex]\sqrt{3}[/tex]/2

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1/1728 is the value of negative integers .

What in math is an integer?

= 12⁻³

= 1/12³

=  1/1728

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Check the picture below.

[tex]~~~~~~\textit{initial velocity in meters} \\\\ S = -5t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&16\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&16\\ \qquad \textit{of the object}\\ h=\textit{object's height}&\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ 0=-5t^2+16t+16\implies 5t^2-16t-16=0 \\\\\\ (5t+4)(t-4)=0\implies t= \begin{cases} -\frac{4}{5}\\\\ 4 ~~ \textit{\LARGE \checkmark} \end{cases}[/tex]

the equation for meters is usually as you see in the picture but for this exercise it got rounded from -4.9 to -5, which is fine.

let's notice that "t"  has two values, however the seconds cannot be a negative value, so we dismiss that one.

The ball will strike the ground 4 seconds after it is thrown When an object is thrown upward, its height , in meters, is given by the quadratic equation S = -5t² + vt + h

To find the time at which the ball will hit the ground, we need to determine when the height (S) of the ball becomes zero. At that moment, the ball will be at ground level.

The height (S) of the ball is given by the quadratic equation:

S = -5t² + vt + h

where:

S = height of the ball in meters

t = time of flight in seconds

v = initial velocity in meters/second (upward velocity, so it's positive)

h = height above level ground from which the object is thrown

Given that the initial velocity (v) is 16 meters/second, and the height above the ground (h) is 16 meters, we can substitute these values into the equation:

S = -5t² + 16t + 16

Now, to find the time (t) at which the ball hits the ground, we need to solve for t when S = 0:

0 = -5t² + 16t + 16

This is a quadratic equation in standard form (ax² + bx + c = 0), and we can solve it by factoring or using the quadratic formula. In this case, let's use the quadratic formula:

The quadratic formula is given by:

t = (-b ± √(b² - 4ac)) / 2a

In our case, a = -5, b = 16, and c = 16. Plugging these values into the quadratic formula:

t = (-(16) ± √(16² - 4*(-5)16)) / 2(-5)

t = (-16 ± √(256 + 320)) / -10

t = (-16 ± √576) / -10

Now, find the two possible solutions for t:

t₁ = (-16 + √576) / -10

t₁ = (-16 + 24) / -10

t₁ = 8 / -10

t₁ = -0.8 seconds

t₂ = (-16 - √576) / -10

t₂ = (-16 - 24) / -10

t₂ = -40 / -10

t₂ = 4 seconds

We have two solutions for t: t = -0.8 seconds and t = 4 seconds. However, we can disregard the negative value for time, as time cannot be negative in this context.

So, the ball will strike the ground 4 seconds after it is thrown.

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Answer:

Step-by-step explanation:

13+(-3)^2+4(-3)+1- {-10-(-6)}

_________________________

[4+5}/ [4^2-3^2(4-3)-8]+12

15/3=5

Answer:

the answer is 18 lol....

Answer:

1/2

Step-by-step explanation:

The probability that student will pass the test is 2/7.

So, the probability that the student will pass the test:

Probability Formula: P(E) = Favourable events/Total events

Now, calculate as follows:

Therefore, the probability that student will pass the test is 2/7.

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Answer: 4.00

Step-by-step explanation:

If the q is 2.00 A to C is double the q. So, 2.00x2= 4.00.

Answer:

Step-by-step explanation:

Given is a parallelogram.

One of the properties of a parallelogram is its diagonals bisect each other.

It gives us:

Step-by-step explanation:

the list of your answer options has a different sequence than the picture.

I assume the picture shows us the correct sequence.

the correct answer is

D : the y-values are all greater than our equal to 2

why ?

because the term in absolute value can only go down to 0 but not below. it is an absolute value after all : it is always positive (minimum 0), no matter what.

so, the minimum value of the function is 0 + 2 = 2. it cannot get lower than this.

Answer: C.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

10th term

Step-by-step explanation:

given [tex]T_{n}[/tex] = 5n + 2 and [tex]T_{n}[/tex] = 52 , then equate right sides and solve for n

5n + 2 = 52 ( subtract 2 from both sides )

5n = 50 ( divide both sides by 5 )

n = 10

that is the 10th term has a value of 52

y = -2x is line parallel to given line.

What is line?

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that are endlessly stretched in the opposing directions.

Main body:

The slope-intercept form is

y=mx+b, where

m is the slope and b is the y-intercept.

y=mx+b

Using the slope-intercept form, the slope is −2.

m=−2

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Use the slope −2 and a given point (0,0) to substitute for

x₁ and y₁ in the point-slope form

y−y₁=m(x−x₁)

, which is derived from the slope equation

m=(y₂−y₁)/(x₂−x₁).

y−(0)=−2*(x−(0))

Simplify the equation and keep it in point-slope form.

y+0=−2⋅(x+0)

Solve for y.

y=−2x

Hence y = -2x is line parallel to given line.

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Answer:

see explanation

Step-by-step explanation:

this can be expressed in ratio form and fractional form , that is

45 : 30 ( divide each part by 15 )

= 3 : 2 ← in simplest form

= [tex]\frac{3}{2}[/tex]

The co-ordinates of the mid-point of the line PQ are (6,4).

From the question, we have

The point P has co-ordinates (10, 12) and the point Q has co-ordinates (2,-4).

Mid-point of the line PQ =(10+2)/2 , (12-4)/2

= (6,4).

Midpoint:

A location in the middle of a line connecting two points is referred to as the midpoint. The midpoint of a line is located between the two reference points, which are its endpoints. The line that connects these two places is split in half equally at the halfway. In addition, the halfway is reached if a line is drawn to divide the line that connects these two places. When we know the coordinates of two points, we can apply the midpoint formula to get the midpoint between them. If we know the coordinates of the other endpoint and the midpoint, we can use the midpoint formula to obtain the coordinates of the endpoint as well.

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The number of students who wore School colors are 8/13. If, Ratio of  students who wore School colors to the number of students who didn't are given.

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or number that is dividing is referred to as the consequent. A ratio compares two numbers by division. A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Given,

Ratio of  students who wore School colors to the number of students who didn't

8:5

Total number of student = 13

Number of students who wore school colors = 8/13

The number of students who wore School colors are 8/13. If, Ratio of  students who wore School colors to the number of students who didn't are given.

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Answer:

Step-by-step explanation:

y= 1/7 - x/7

Answer:

y = 1/7 - x/7

Step-by-step explanation:

4(7y + x) = 4             Distribute the 4 to 7y and x

28y + 4x = 4            Subtract the 4x on both sides

28y = 4 - 4x            To get 'y' by itself divide 28 on both sides

y = 4/28 - 4x/28      You can simplify the 4/28 since 4 goes into 28 7 times

y = 1/7 - x/7

The amount of interest to be charged on the note, based on the face value of the note, is $302. 22.

The amount the borrower would receive is $16, 697. 78.

The interest charged on the simple discount note can be found by the formula:

= Face value of note x discount rate x number of days / total days in a year

= 17, 000 x 4% x 160 / 360

= $302. 22

The amount that the borrower would receive is then:

= Face value of note - Interest charged on note

= 17, 000 - 302.22

= $ 16, 697. 78

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The probability of picking a shirt that is red or striped is 2/3.

Given, that a drawer of shirts contains 3 solid red, 2 striped red, 4 solid blue, and 3 striped green.

We have to find the probability of picking a shirt that is red or striped,

P(R ∪ S) = P(R) + P(S) - P(R∩S)

where, R be the event that the shirt is red.

and S be the even that the shirt is striped.

P(R) = 5/12 (as, there are 5 red shirts)

P(S) = 5/12 (as, there are 5 striped shirts)

P(R∩S) = 2/12 (as, there are 5 striped red shirts)

P(R ∪ S) = 5/12 + 5/12 - 2/12

P(R ∪ S) = 8/12

P(R ∪ S) = 2/3

The probability of picking a shirt that is red or striped is 2/3.

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Using the sum of exterior angle, the value of n is 11.

In the given question,

A hexagon has exterior angle measures of (7n + 3), (10n-17), (8n - 16), (4n+17), (-n + 16), and (5n - 6)°.

We have to find the value of n.

As we know that the sum of exterior angle of any polygon is equal to 360°.

As the given measures are (7n + 3), (10n-17), (8n - 16), (4n+17), (-n + 16), and (5n - 6)°.

So we can find the value of n by adding the all measures.

So the expression should be

(7n + 3) + (10n-17) + (8n - 16) + (4n+17) + (-n + 16) + (5n - 6)° = 360°

Simplifying the bracket.

7n + 3 + 10n-17 + 8n - 16 + 4n+17 - n + 16 + 5n - 6 = 360°

Solving the expression by solving the same term

(7n+10n+8n+4n-n+5n)+(3-17-16+17+16-6)= 360°

33n-3 = 360°

Add 3 on both side

33n-3+3 = 360°+3

33n = 357°

Divide by 33 on both side

33/33 n= 363°/33

n = 11

Hence, the value of n is 11.

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-6t -54  is the expression equivalent to-6(t+9)

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s)

Given: -6(t+9)

First, clear the parenthesis by using -6 to multiply t and 9:

-6(t+9) = (-6 x t) + (-6 x 9)

          = -6t + (-54)

          = -6t -54

Therefore, the -6t -54 is equivalent to -6(t+9)

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Quadratic equation that passes through the points (-4,2) and (2,2) and a form a graph of horizontal line y =2.

Given,

Quadratic equation passes through the points (-4,2) and (2,2)

(x₁, y₁) =(-4,2)

(x₂ ,y₂) = (2,2)

Here,

(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)

⇒(y - 2) / (x + 4) = (2 -  2) / (2 + 4)

⇒ (y-2) / (x+4) =0

⇒y -2 =0

⇒y = 2

Quadratic equation formed from the given points (-4,2) and (2,2) is y =2.

Which represents the horizontal line and does not have any vertex.

Therefore, quadratic equation that passes through the points (-4,2) and (2,2) and a form a graph of horizontal line y =2.

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The cost per mile incurred by Ernest Dorsey for driving the sports coupe for last year was $0.41.

The cost per mile is the quotient of the division operation involving the total cost incurred and the driving mileage for the year.

To derive the total cost, add up the value of the car consumed (cost - current value), the annual variable, and fixed costs.

Cost of a used sports coupe last year = $8,000

The current value of the car = $6,000

Used value for the year = $2,000.00 ($8,000 - $2,000)

Gasoline               $1,589.56

Oil changes            $245.98

Repairs                     $548.11  $2,383.65

Insurance             $1,105.32

License                    $85.00    $1,190.32

Total cost for the year =        $5,573.97

Driven mileage for the year = 13,569 miles

Cost per mile = $0.41 ($5,573.97/13,569)

Thus, the cost per mile is $0.41.

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The simplified value of the above expression is 5.00248967e-19

we know,'^' this symbol means by times

[tex]3^{3}[/tex] =27

[tex]6^{6}[/tex] =46,656

27 multiplied by 46,656

[tex]27 \times 46,656 = 1,259,712[/tex]

[tex]1,259,712 ^{-3} = 5.00248967e-19[/tex]

if you want you can apply the BODMAS  system here.

it is just a fraction try to simplify it.

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The student pay initial fess of $20 and addition $10 per hour.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

Plan 1:

students pay = $15 per hour.

Plan 2:

From the graph we can see that

slope= Rise/ Run = 10/ 1= 10

and, the graph line starts from 20.

Hence, the student pay initial fess of $20 and addition $10 per hour.

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Given the table on the total money earned, the type of association the scatter plot would represent is 2. A positive linear association

When two variables are said to have a positive linear association, it means that they move in the same direction together. When one of them increases, the other increases as well. It also means that they are increasing by a uniform amount. For instance, when one variable increases by 3, the other increases by 6, always.

The hours worked here are increasing as well as the money earned by Jacob. The hours worked is increasing by 1, and the money earned is increasing by 4. This is therefore a positive linear association.

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